Analyses of growth curves of nellore cattle by multiple-trait and random regression models

The purpose of this study was to compare estimates of genetic parameters for sequential growth of beef cattle using two models and two data sets. Growth curves of Nellore cattle were analyzed using body weights measured at ages 1 (birth weight) to 733 d. Two data samples were created, one with 71,867 records sampled from all herds (MISS), and the other with 74,601 records sampled from herds with no missing traits (NMISS). Records preadjusted to a fixed age were analyzed by a multiple-trait model (MTM), which included the effects of contemporary group, age of dam class, additive direct, additive maternal, and maternal permanent environment. Analyses were by REML, with five traits at a time. The random regression model (RRM) included the effects of age of animal, contemporary group, age of dam class, additive direct, additive maternal, permanent environment, and maternal permanent environment. All effects were modeled as cubic Legendre polynomials. These analyses were also by REML. Shapes of estimates of variances by MTM were mostly similar for both data sets for all except late ages, where estimates for MISS were less regular, and for birth weight with MISS. Genetic correlations among ages for the direct and maternal effects were less smooth with MISS. Genetic correlations between direct and maternal effects were more negative for NMISS, where few sires were maternal grandsires. Parameter estimates with RRM were similar to MTM cept that estimates of variances showed more artifacts for MISS; the estimates of additive direct-maternal correlations were more negative with both data sets and approached -1.0 for some ages with NMISS. When parameters of a growth model obtained by used for genetic evaluation, these parameters should be examined for consistency with parameters from MTM and prior information, and adjustments may be required to eliminate artifacts.     

Genetic evaluation of growth in nellore cattle by multiple-trait and random regression models

The objective of this study was to identify issues in genetic evaluation of beef cattle for growth by a random regression model (RRM). Genetic evaluation data included 2,946,847 records of up to nine sequential weights of 812,393 Nellore cattle measured at ages ranging from birth to 733 d. Models considered were a five-trait multiple-trait model (MTM) and a cubic RRM. The MTM included the effects of contemporary group, age of dam class, additive direct, additive maternal, and maternal permanent environment. Both additive effects were assumed correlated. The RRM included the same effects as MTM, with the addition of permanent and random error effects. The purpose of the random error effect, which was in addition to a residual effect with constant variance, was to model heterogeneous residual variances. All effects in RRM were modeled as cubic Legendre polynomials. Expected progeny differences (EPD) were obtained iteratively using a preconditioned conjugate gradient algorithm. Numerically accurate solutions with RRM were not obtained until the random regressions were orthogonalized. Computing requirements of RRM were reduced by more than 50%, without affecting the accuracy by removing regressions corresponding to very low eigen-values and by replacing the random error effects with weights. Afterward, the correlations between EPD from RRM and from MTM for EPD on selected weights were between 0.84 and 0.89. For sires with at least 50 progeny, these correlations increased to 0.92 to 0.97. Low correlations were caused by differences in parameters. The RRM applied to growth i s prone to numerical problems. Estimates of EPD with RRM may be more accurate than those with MTM only if accurate parameters are applied.     

Genetic parameters estimated with multitrait and linear spline-random regression models using Gelbvieh early growth data

Estimates of direct and maternal genetic parameters in beef cattle were obtained with a random regression model with a linear spline function (SFM) and were compared with those obtained by a multitrait model (MTM). Weight data of 18,900 Gelbvieh calves were used, of which 100, 75, and 17% had birth (BWT), weaning (WWT), and yearling (YWT) weights, respectively. The MTM analysis was conducted with a three-trait maternal animal model. The MTM included an overall linear partial fixed regression on age at recording for WWT and YWT, and direct-maternal genetic and maternal permanent environmental effects. The SFM included the same effects as MTM, plus a direct permanent environmental effect and heterogeneous residual variance. Three knots, or breakpoints, were set to 1, 205, and 365 d. (Co)variance components in both models were estimated with a Bayesian implementation via Gibbs sampling using flat priors. Because BWT had no variability of age at recording, there was good agreement between corresponding components of variance estimated from both models. For WWT and YWT, with the exception of the sum of direct permanent environmental and residual variances, there was a general tendency for SFM estimates of variances to be lower than MTM estimates. Direct and maternal heritability estimates with SFM tended to be lower than those estimated with MTM. For example, the direct heritability for YWT was 0.59 with MTM, and 0.48 with SFM. Estimated genetic correlations for direct and maternal effects with SFM were less negative than those with MTM. For example, the direct-maternal correlation for WWT was -0.43 with MTM and -0.33 with SFM. Estimates with SFM may be superior to MTM due to better modeling of age in both fixed and random effects.     

Study of codes of disposal at different parities of Large White sows using a linear censored model

To study the genetic relationship between three grouped reasons for sow removal (SR) in consecutive parities, accounting for censoring, 13,838 records from Large White sows were analyzed. Data were from seven pure-line farms having, on average, 5.9% unknown SR. Three traits were subjectively defined, each corresponding to a classification of SR (reproductive [RR], nonreproductive [RN], and others [RO]). Records for each trait could take one of five categories, according to parity at removal (0 to 4 or later). A multivariate linear censored model was implemented. The model to estimate (co)variance components and parameters included the effects of year-season, region, contemporary group, and additive genetic effects. The most common SR was related to reproduction (48.5%). Diseases of different origin and cause, old age/parity, and sow death or loss accounted for about 18, 7, and 4% of total culls, respectively. Estimates of variance components showed heterogeneity of additive genetic and residual variances for the three traits. Estimates of heritability were 0.18, 0.13, and 0.15 for RR, RN, and RO, respectively. Genetic correlations between removal codes were high (> or =0.90). Results suggest sizeable additive genetic variances exist for parity at removal and different codes of removal. Different SR reasons seem to operate similarly or as a closely related genetic trait associated with fitness. In particular, RN and RO seem to be genetically indistinguishable. Data structure, definition, and volume are major limitations in studies of sow survival. A multiple-trait censored model is preferred to evaluate reasons of sow disposal. Grouped removal causes seem to be strongly genetically correlated but with heterogeneous variances, suggesting that combining all removal causes and treating the trait as parity at disposal is an alternative approach.     

Estimation of additive and nonadditive genetic variances in Hereford, Gelbvieh, and Charolais by Method R.

Parameters for direct and maternal dominance were estimated in models that included non-additive genetic effects. The analyses used weaning weight records adjusted for age of dam from populations of Canadian Hereford (n = 467,814), American Gelbvieh (n = 501,552), and American Charolais (n = 314,552). Method R estimates of direct additive genetic, maternal additive genetic, permanent maternal environment, direct dominance, and maternal dominance variances as a proportion of the total variance were 23, 12, 13, 19, and 14% in Hereford; 27, 7, 10, 18, and 2% in Gelbvieh; and 34, 15, 15, 23, and 2% in Charolais. The correlations between direct and maternal additive genetic effects were -0.30, -0.23, and -0.47 in Hereford, Gelbvieh, and Charolais, respectively. The correlations between direct and maternal dominance were -0.38, -0.02, and -0.04 in Hereford, Gelbvieh, and Charolais, respectively. Estimates of inbreeding depression were -0.20, -0.18, and -0.13 kg per 1% of inbreeding for Hereford, Gelbvieh, and Charolais, respectively. Estimates of the maternal inbreeding depression were -0.01, -0.02, and -0.02 kg, respectively. The high ratio of direct dominance to additive genetic variances provided some evidence that direct dominance effects should be considered in beef cattle evaluation. However, maternal dominance effects seemed to be important only for Hereford cattle.     

Constructing covariance functions for random regression models for growth in Gelbvieh beef cattle

Genetic parameters for a random regression model of growth in Gelbvieh beef cattle were constructed using existing estimates. Information for variances along ages was provided by parameters used for routine Gelbvieh multiple-trait evaluation, and information on correlations among different ages was provided by random regression model estimates from literature studies involving Nellore cattle. Both sources of information were combined into multiple-trait estimates; corrected for continuity, smoothness, and general agreement with literature estimates; and extrapolated to 730 d. Covariance functions using standardized Legendre polynomials were fit for the following effects: additive genetic (direct and maternal), and animal and maternal permanent environment. Residual variances at different ages were fitted using linear splines with three knots. Fit was by least squares. The order of polynomials was varied from third to sixth. Increasing the fit beyond cubic provided small improvements in R2 and increased the number of small eigenvalues of covariance matrices, especially for the additive effect. Parameters for a random regression model in beef cattle can be constructed with negligible artifacts from literature estimates. Formulas can easily be modified for other types of polynomials and splines.     

Technical note: Computing options for genetic evaluation with a large number of genetic markers

Two simulated data sets and one commercial data set were used to evaluate computing options for models in which the effects attributable to QTL were fit as covariables. The simulated data sets included records on 24,000 animals for 10 traits. Data sets 1 and 2 were simulated with low and high correlations among traits, respectively. The model included an overall mean, 160 covariables as effects attributable to QTL, the random animal genetic effect, and the random residual effect. A commercial data set included records on approximately 110,000 animals for 11 growth, reproduction, and other traits. The model included the effects usually fitted for these traits as well as 116 covariables as effects attributable to QTL; models including the number of covariables varied by trait. Initial computing was by the BLUP90IOD program, which applies iterations on data by using a preconditioned conjugate gradient algorithm with a diagonal preconditioner. Modifications included adding block preconditioners for effects attributable to QTL (BQ) and for traits (BT). With the simulated data sets and the original program, one-trait analyses without the covariables took 7 s, whereas the 10-trait analyses with the covariables took 15 min for a data set with low correlations and 1 h 40 m for a data set with high correlations. The BQ improved the convergence rate but increased the computing time. The BT decreased the computing time from 1.5 times (low correlations) to 7 times (high correlation) at a cost of greater memory requirements. For the commercial data and the complete model, computing took 10.3 h with the unmodified program and was reduced to 6 h with BT. Relative changes in computing time and convergence rate with the commercial data set were close to those of the simulated data set, with low correlations among the traits. The BQ decreased the number of rounds by less than expected. Genetic evaluation with a large number of effects attributable to QTL fit as covariables is feasible.     

Genetic study of individual preweaning mortality and birth weight in Large White piglets using threshold-linear models

Individual records from 49,788 Large White piglets were used to evaluate preweaning mortality and its relationship with birth weight (BW). Preweaning mortality included farrowing mortality (TM) was also divided into stillbirth (SB), early (EM), late (LM) and total (ELM) preweaning mortality. Farrowing mortality was also studied as a sow's trait as number of piglets born dead (NBD). Threshold-linear models were used via MCMC. Traits included (1) TM-BW, (2) SB-ELM-BW, (3) SB-EM-LM and (4) NBD-ELM-BW. Model for BW included parity number, litter size, sex, contemporary group (farm-farrowing year-month), litter, and direct and maternal additive genetic effects. For mortality traits, litter effect was of the nursing litter for cross-fostered piglets (4.9%). Models for SB (2, 3) and NBD (4) excluded the effect of sex. In Model 3, BW was fitted as covariable for EM and LM. Estimates of direct and maternal heritability for BW were 0.03–0.06 and 0.14–0.19; and for mortality traits 0.03–0.12 and 0.08–0.12. Direct-maternal correlations were negative for all traits. Genetic correlations between all mortality traits were positive. Results confirmed the importance of BW for the genetic evaluation of piglet mortality. Early mortality is a good candidate for improvement of TM because of larger heritability and high genetic correlations with other mortality traits. It is most efficient to treat SB at sow level and preweaning mortality at the piglet level.     

Genetic correlations between two strains of Durocs and crossbreds from differing production environments for slaughter traits

The aim of this study was to estimate the genetic correlations between 2 purebred Duroc pig populations (P1 and P2) and their terminal crossbreds [C1 = P1 x (Landrace x Large White) and C2 = P2 x (Landrace x Large White)] raised in different production environments. The traits analyzed were backfat (BF), muscle depth (MD), BW at slaughter (WGT), and weight per day of age (WDA). Data sets from P1, P2, C1, and C2 included 26,674, 8,266, 16,806, and 12,350 animals, respectively. Two-trait models (nucleus and commercial crossbreds) for each group included fixed (contemporary group, sex, weight, and age), random additive (animal for P1 and P2 and sire for C1 and C2), random litter, and random dam (C1 and C2 only) effects. Heritability estimates (+/-SE) for BF were 0.46 +/- 0.04, 0.38 +/- 0.02, 0.32 +/- 0.02, and 0.33 +/- 0.02 for P1, P2, C1, and C2, respectively. Heritability estimates for MD were 0.31 +/- 0.01, 0.23 +/- 0.02, 0.19 +/- 0.01, and 0.12 +/- 0.01 for P1, P2, C1, and C2, respectively. The estimates for WGT and WDA were 0.31 +/- 0.01, 0.21 +/- 0.02, 0.16 +/- 0.01, and 0.18 +/- 0.01 and 0.32 +/- 0.01, 0.22 +/- 0.02, 0.16 +/- 0.01, and 0.19 +/- 0.01, respectively. Genetic correlations between purebreds and crossbreds for BF were 0.83 +/- 0.09 (P1 x C1) and 0.89 +/- 0.05 (P2 x C2), for MD 0.78 +/- 0.05 (P1 x C1) and 0.80 +/- 0.08 (P2 x C2). For WGT and WDA, the correlations were 0.53 +/- 0.08 (P1 x C1), 0.80 +/- 0.10 (P2 x C2), and 0.60 +/- 0.07 (P1 x C1) and 0.79 +/- 0.09 (P2 x C2), respectively. (Co)variances in crossbreds were adjusted to a live BW scale. Compared with purebreds, the genetic variances in crossbreds were lower, and the residual variances were greater. Sire variances in crossbreds were approximately 20 to 30% of the animal variances in purebreds for BF and MD but were 13 to 25% for WGT and WDA. The efficiency of purebred selection on crossbreds, assessed by EBV prediction weights, ranged from 0.43 to 0.91 for line 1 and 0.70 to 0.92 for line 2. When nucleus and commercial environments differ substantially, the efficiency of selection varies by line and traits, and selection strategies that include crossbred data from typical production environments may therefore be desirable.